Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1, 5). What are the coordinates after the two transformations: Translation (x, y) --> (x - 2, y - 1) Rotation: 90 degrees counterclockwise at the origin. Immersive Reader

Given :

Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1, 5).

To Find :

The coordinates after the two transformations:

a) Translation (x, y) --> (x - 2, y - 1) .

b)  Rotation: 90 degrees counterclockwise at the origin.

Solution :

Applying transition a) , we get :

R'(2-2,3-1) , S'(-2-2,1-1) , T'(-1-2,5-1)

R'( 0, 2) , S'( -4 , 0), T'( -3, 4)

Now , When any point ( h , k ) is rotated 90° counterclockwise about the origin, the new points are (-k , h) .

So , R''( -2, 0) , S''( 0, -4 ) , T''( -4 , -3 ) .

Therefore , the coordinates after transformations are

( -2, 0) ,( 0, -4 ) , ( -4 ,-3 ) .

Hence , this is the required solution .